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arXiv:2605.10472

Influence of pump size on pattern formation in exciton-polaritonic Bose-Einstein condensates in the non-Markovian regime

N. V. Kuznetsova, A. D. Alliluev, D. V. Makarov, A. A. Anisich

cond-mat.quant-gascond-mat.stat-mechnlin.PSphysics.opticsquant-phSubmitted May 11, 2026• Announced May 12, 2026• 0 citations• Revised May 12, 2026 (v2)
v1 · May 11, 2026v2 · May 12, 2026
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Abstract

Dynamics of exciton-polaritonic condensate under incoherent pumping is studied using the non-Markovian stochastic Gross-Pitaevskii equation with the pseudo-differential dispersion term. This term corresponds to the lower energy branch of polaritons. It is shown that an increasing of the pumping spot area leads to the appearance of various spatial structures whose properties depend on the duration of the dynamical memory. In the regime of short memory time, condensate can form an extended state that spans outside the pumping area. We conclude that onset of such extended states is related to the specific form of the dispersion term causing the ``traffic jam'' effect. The case of long memory time corresponds to enhanced condensate formation, when increasing of the pumping area leads to appearance of angular condensate structures which partially suppress emission of matter waves from the pumping area.

Comments
9 pages, 5 figures

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Dynamics of exciton-polaritonic condensate under incoherent pumping is studied using the non-Markovian stochastic Gross-Pitaevskii equation with the pseudo-differential dispersion term. This term corresponds to the lower energy branch of polaritons. It is shown that an increasing of the pumping spot area leads to the appearance of various spatial structures whose properties depend on the duration of the dynamical memory. In the regime of short memory time, condensate can form an extended state that spans outside the pumping area. We conclude that onset of such extended states is related to the specific form of the dispersion term causing the ``traffic jam'' effect. The case of long memory time corresponds to enhanced condensate formation, when increasing of the pumping area leads to appearance of angular condensate structures which partially suppress emission of matter waves from the pumping area.
Dynamics of exciton-polariton condensates under continuous-wave incoherent Gaussian optical pumping is considered. It is shown that the conventional supercritical Stuart-Landau picture is invalid in a certain domain of the parameter space. For strong polariton repulsion from the reservoir and relatively small pump spots, the dynamics is adequately described by the quintic Stuart-Landau equation. The corresponding subcritical pitchfork bifurcation leads to condensate formation, accompanied by bistability between the trivial and nontrivial states over a finite pump-power range and a one-bit memory. Further increase of the repulsion parameter or decrease of the spot size breaks down the perturbative approach and leads to a peculiar self-trapping regime with complex dynamics. Experimental evidence of the emergence of the proposed behavior is provided. Our findings can be used to design polaritonic setups that exploit the predicted memory effect.
Abstract The dynamics of an exciton–polariton Bose–Einstein condensate in an optical microcavity was considered. A novel version of the stochastic Gross–Pitaevskii equation was proposed to describe the condensate evolution under the non-Markovian interaction with the environment. The proposed version was used to analyze the condensate dynamics at various temperatures. The phase transition from the homogeneous to the fragmented state of the condensate near a temperature of 15 K was detected. This phase transition is accompanied by a sharp drop in the condensate density and a decrease in the correlation length. It was found that, at a temperature of 10 K, the correlation length oscillates with time. The results obtained indicated the necessity to take into account the non-Markovianity of the condensate interaction with the excitonic reservoir.
Dynamics of exciton-polariton Bose‒Einstein condensate in an optical microcavity is considered. A novel version of stochastic Gross‒Pitaevsky equation for description of condensate evolution under non-Markovian interaction with environment is proposed. Using the proposed version, analysis of condensate dynamics for various temperatures is carried out. The phase transition from a homogeneous to fragmented condensate state near temperature of 15 K is found. This phase transition is accompanied by drop of condensate density and decrease of correlation length. It is found that correlation length oscillates with time for the temperature of 10 K. The results obtained indicate the necessity to take into account non-Markovianity of condensate interaction with the excitonic reservoir.
We investigate the stability and coherence properties of one-dimensional exciton-polariton condensates under nonresonant pumping. We model the condensate dynamics using the open-dissipative Gross-Pitaevskii equation. In the case of spatially homogeneous pumping, we find that the instability of the steady state leads to significant reduction of the coherence length. We consider two effects that can lead to the stabilization of the steady state, i.e., the polariton energy relaxation and the influence of an inhomogeneous pumping profile. We find that, while the former has little effect on the stability, the latter is very effective in stabilizing the condensate, which results in a large coherence length.
Exciton-polariton Bose-Einstein condensates (BECs) are newly emerged quantum systems that are capable of showing macroscopic quantum phenomena with intrinsic open-dissipative nature. The spatial distribution of the polariton density, without any external potential, can be controlled by the geometric shape of the pumping laser, enabling the investigation of polariton dynamics with topologically non-trivial configurations. Meanwhile, exciton-polaritons have spin degrees of freedom inherited from excitons and photons, making it a candidate for the realization of quantum logic gates. In this thesis, we will investigate theoretically the nonlinear dynamics of exciton-polariton BECs involving both polaritons' spatial degrees of freedom and spin degrees of freedom, and interactions between them. This thesis is organised as follows: In Chapter 1, we will present an overall review of exiton-polariton systems and important properties of polariton BECs and then introduce the dynamical equations with various interactions that will serve as the main theoretical tool for subsequent chapters. Several polariton pumping and trapping techniques appearing in later chapters will also be introduced. In Chapter 2, we will investigate the superfluidity properties of a single-component polariton condensate under an incoherent annular pumping configuration. By studying the stability properties of polariton persistent currents, we find that the persistent currents can exhibit dynamical instability and energetic-like instability according to different parameter region. A stability phase diagram will be given and its relation with the Landau's criterion will be discussed. In Chapter 3, we will investigate the spin dynamics of a two-component polariton condensate under a homogeneous pumping configuration. Owing to the Josephson coupling, there exist multiple steady state solutions that allow of controlled spin state switching. A desynchronized region where there exists no stable steady solution is found. In the desynchronized region, a desynchronized state beating periodically over time can exist, which will serve as a building block of spin waves presented in the next chapter. In Chapter 4, by combining results from the previous two chapters we will investigate generally the nonlinear dynamics of polariton condensates under an annular pumping configuration. The spin-orbit interaction provided by the Josephson coupling supports azimuthon states that have simultaneous modulations in both amplitude and phase. The azimuthon states, when viewed in a different polarization basis, form rotating spin waves that can be referred to as the optical ferris wheel. In Chapter 5, results from previous chapters will be extended to micocavities that support the anisotropic TE-TM splitting interaction. Rotating singularities (small-scale vortices) are found as a result. Their properties and experimental observation techniques will be discussed. Chapter 2-5 provide a theoretical framework for the nonlinear dynamics of polariton condensates. They rely mostly on optical trapping techniques and are ready to be tested in experiments. In Chapter 6, polaritons trapped by an engineered periodic mesa potential will be discussed. We will investigate the band structure of polaritons under the influence of the periodic potential together with discussions on the phase-modulated interference pattern which corresponds to the polariton Talbot patterns observed in experiments.
We report an experimental study of the spontaneous spatial and temporal coherence of polariton condensates generated in the optical parametric oscillator configuration, below and at the parametric threshold, and as a function of condensate area. Above the threshold we obtain very long coherence times (up to 3 ns) and a spatial coherence extending over the entire condensate (40 μm). The very long coherence time and its dependence on condensate area and pump power reflect the suppression of polariton-polariton interactions by an effect equivalent to motional narrowing.